 Any questions? Anybody besides Joe, to look at the swinging chair problem from yesterday, that most awesome of all amusement park rides ever, certainly better than that turntable one where they drop out the floor and it makes you sick in front of your astronaut brother in a lot of ways it really looks stupid. We'll get to that one later. Do you really don't have an astronaut brother in a lot of ways? No, because he quit and is now teaching at the Naval Postgraduate School. He's been up on two shuttle missions and won six months stay on the space station, which meant once, every hour and a half, he was closer to me than he ever has been any other time to do. It's only like 260 miles overhead. Anyway, that's my trial. Life. What do astronauts do with their astronauts? Drag, mostly. I pick up girls in bars, I think, and put on weight. Only Joe looked at that. Only Joe has a question about that swinging chair thing, man. All right, Joe. There you go. Check it out there. All right. Any other open questions, though, before we get going here? All right. What we're looking at, if you remember, are different types of forces because our number one tool right now for solving kinetics problems is Newton's law. F equals ma. By f, I'm being a little bit loose. I mean, the sum of the forces. A lot of times in our problems, there's just one. But if there's more than one, it's no big deal. We add them all up. It's all the forces together. And whatever's left over, if anything, that will determine if there's any acceleration. So we looked at some tributal force yesterday. Did we talk about spring force a little bit? I think I did just real quick. And there's a business in the book about it. Everybody's played with springs before. It's not like you don't know what they do. You just may not know how to quantify it. It's pretty straightforward. So we'll spend a little bit of time on some other things as we go here. So what we're going to look at today, well, let's do a little force experiment here and see what's going on if we can all figure it out. Very simple setup. I've just got a little block of wood that's on the table. I attach a string to it. We know what strings do. They only pull. And then I've got a scale here to help me determine what's going on. So I'm going to put it there. Let's see. What's this reading? This reads in Newtons. So I'm pulling with pretty much all my might right now. Three Newtons. I should probably push my sleeve up so you can see the veins. No, you feel to see from there where he was. He could actually see it pushing out against my shirt. Oh man, that shirt ripped open. I'm going to lose my eyesight or something. So about three Newtons. So let's see. Let's draw a free body diagram of that setup. The string is pulling on this little block with the weight on it by about three Newtons. We read that right off the scale. Any other forces on it? Who's going to leap forward and take the easy one? Who did that? Nobody? Nobody wants to put somebody on there? Yeah, well wait. See, you got to be smart here and always jump in and get the easy one right off the bat. I've got about 2,000 grams on there. And then that then weighs maybe 100 or 200 grams or so. Any other forces? The normal force. Otherwise, the weight would accelerate it down. So there's got to be a normal force. In fact, in this case, we figure unless there's some other vertical forces that we don't have up there, and I can't imagine what they would be, then in this case, the normal force equals the weight. Not always. We need a free body diagram to check to make sure whether it does or not. But in this case, the weight and the normal force happen to be equal in opposite. So I'm pulling on it to the right with three Newtons, but it was not accelerated. The only way that can be, oh, all the way up to four now, it's not accelerating. Listen, if it's not accelerating, if I sum the forces in the x direction, we'll let that be the x direction, that be the y direction. As usual, if we don't have to specify it, we'll just take it as that, I guess. There happens to be no x acceleration. Well, wait, how do I know there wasn't any x acceleration? I mean, did I measure it? Did I run a little ticker-tape thing through it? Wow, that high-sounding. Because it was just sitting there, and that's all it was doing. If it was accelerating, we'd see it do something else a second later. That's what Mike meant, but he wanted to sound more important than that. So the forces then must also sum to zero. Here's our first indication, at least in a quantifiable term, what you all know to be going on anyway. In fact, I think I heard someone say it. What's the force that's missing? Clearly, we don't have all the forces. Because I don't have any force up here that balances this one. There's got to be another one that balances, at least one more, that balances this force is equal and opposite in the other direction. Somebody said it. Who said it? Friction. It's friction. Obviously, friction is pulling back in that way. We typically, just to remind this, it's a different force, and so we don't just treat it like other ones because we're going to have to do some other stuff with it here in a minute. Give it that little sort of script F for friction. Now, the interesting thing is, it appears to be adjustable. See, I pull with three Newtons. The friction must be three Newtons. I go up to four Newtons. The friction must be four Newtons. Five. I try to trick it. I go back down to four. It catches that. I try to trick it. I try to distract it. I say, hey, look over there. To five, it knows. It's reading my mind. It knows what I'm doing. If we graph this, let's see. Here's the force I'm applying. And I tried three Newtons. I couldn't get much below three Newtons because then just the weight of the scale itself tends to pull down too much. There's not even enough tension in the line to hold that. I have the force I apply across there and the friction I calculate there. I'm not measuring the friction. I'm calculating it. All I can do is sum the forces in the x direction. I know what I'm doing and I know the friction's opposing it. If I do three Newtons, then friction does up to four Newtons. And if it doesn't know, I was doing four Newtons. Here, you know what? It's peaking. So I'm going to cover you. Okay, Joey, get ready. Damn it, Newtons. It knows what I'm going to do. If I go to five Newtons, I hate this. I can't get you guys to know what I'm talking about half the time and this thing's reading my mind. It's going to hate that. It knows what I'm doing. One for one. What's the slope of that line? One. That slope of that line is perfectly one. Not sort of one. Not occasionally not one. Not one for me and 1.1 for you. Because if that slope was anything other than one, then either this force would be bigger than this one or this one would be bigger than that one. And that thing would start to accelerate. It's perfectly one. It knows exactly what I'm going to do. Even everywhere in between. Because this is an analog scale. Everybody know what that is? Analog scale. Analog is a scale that can read any possible value. Whereas a digital scale could only read certain values. This is an analog scale. Not only do I get three Newtons, four Newtons, five Newtons, I can hit absolutely every little miniature tiny bit of a Newton in between. Six. A new record. Guys, things are reading my mind. It's perfectly reading my mind. It's really reading my mind. It knows exactly how much force I apply. It won't apply anymore. And it won't apply any less. So I go to... Ah! Something happened there. Something where did it happen, Joey? It happened about seven. Well now we got things going. Now things are sliding a little bit. There's a lot of shock all over here. So now, some time or other, I get to a point where I can actually pull it hard enough and it starts to accelerate now. You know what? I think we had a goober right there stuck on. But you know what? That's important to us. We need to know why it moves and why it doesn't. So now, it looks like we can't hit five or six anymore for some reason. Now it starts to move. Unfortunately, I don't have this table I want. There's five. Hit five a little bit. Oh, and then they even drop down. Got the five. Drop down a little bit. So clearly, there's a limit. And you know this. If you've ever tried to push a couch across the floor or something, you got to... If you don't push hard enough, it doesn't go. You got to push harder and harder until it starts to go. And then once you finally get it going, what happens? Huh? You ever move the couch? Yeah, it's actually... Once it gets moving, isn't it actually easier? Some, there's just too much garbage on the floor there. Sooner or later, it breaks free and the friction force actually drops down. And as we apply more force, now it starts to accelerate. That's much harder to work with because we have to test, well, how much force do I have to apply for constant velocity where I can have it moving but not accelerating or how much force do I have to apply to get it to accelerate? It's a much trickier thing. But what we find is once it's moving, if we could be sense enough to do that test, we find that the friction force would never change and we can very easily get above the friction force, give that thing some pretty good acceleration. So it appears that we've got two things going on. We had this region where nothing would move. That's when I couldn't pull it hard enough to get it to move, but it always pulled it back exactly what I did every time it pulled back against me. Then we had this region here where the friction force actually drops down. You know that from shoving couches across the floor or whatever it is you were trying to steal that day where actually things are moving. This is a static region. Static means no acceleration or no movement. This is a kinetic region where things are moving. So we did that before and then we got up to five and then it started moving and then things got a little goofy here on the surface somehow. I'm not sure why. Now we could get things moving. So let's see if we can try something out. Let's get a reading here with our new slippery surface, whatever it is happening. So about four and a half. Right, Joe? And then things start to move. I'm a little less there. Not big news, is it? Isn't it easier to slide? When you need to slide your couch across the floor, do you want your drunk uncle Earl sleeping on the couch when you do that? Oh, you said get your butt off. Go get a job. I got to move the couch because the couch is moving. You don't want to push Uncle Earl across the floor because he's going to make it too hard to push that. So it seems like friction has something to do with the weight. Is that seem reasonable? If I put both of these on, what were we at with just this one, Joe? Four and a half? And then you see when it started to move, you see it drop down pretty hard. This is a real rough set. But now we're all way up to six or something. And here's the friction. Well, not the friction. The static friction is always one for one. No matter how much I'm towing, isn't it? Because I never have any acceleration. No matter what I'm trying to tow, I never have acceleration. Whether I'm here or whether I take that one off, as long as I'm not moving, I must not have any, it's always one for one. But here's like this highest point I have to pull. Might have something to do with the weight. Is that what seems like? The heavier it is, the higher I have to go, the higher the load I have to exert before it will finally break free. Does that seem reasonable? Maybe we draw it to something like this. Here's my force. There's friction force. If I don't have very much weight on there, just the one little one, then I don't have to pull very hard before it breaks loose. But if I have more weight on there, I've got the big one, or I've got the two of them together, it appears like I've got to go a little bit farther before it breaks loose. Before that, to the left of that peak, it's always one to one. Friction's always one to one with my pull, because that's the zone where it's not accelerated. So it's this peak here that seems to be of interest. How can we predict what that peak is going to be? Before that, there's nothing to predict. It's doing the predicting. It's one for one what I applied. I applied three, it applies three. I applied 3.269, it applies 3.269 back. But that peak, this, let's call it, let's call it the maximum static friction. Maximum friction, that's the maximum force I can apply before it finally breaks loose and is no longer in the static region, it's down in the kinetic region, because it's starting to move. If it's starting to move and it wasn't before it accelerated. It seems like that point would be of interest. Maybe it's not something you'd actually calculate when you're trying to move your couch, but if you're trying to calculate whether you've got a good design for snow tires or how much friction is in a machine in the bearings or in the belts or something when you're part of that engineering design team, it seems like that kind of thing might be of interest to you. What is this maximum static friction? If you can calculate it, then you can take it into your design calculations to do a better design. It seems like it has something to do with the weight, doesn't it? So we'll put a question mark there because it seems like it has something to do with the weight. Try it again. I've got the weight down, I'm there, and what we're trying to find out is what's the maximum force I have to apply to finally get the surfaces to break loose and the object starts to accelerate. It doesn't accelerate for long because I can't pull it very far before it's off the table. But once it's at that maximum amount I have to pull, I know that friction is at its maximum amount because until that point, they're one for one. So it's very easy for me to indirectly measure the friction. I'm looking to see when's the maximum static friction. Clearly, just double check. It's not accelerating up or down. There must be some normal force up that's equal to the weight. And I'm looking now what's the maximum force I apply because that's the maximum force that the friction reapplies back against me just until it takes me to break the surfaces loose. So now I'm going to do a test, a little bit of a test here. I just want to double check something. All right, here we go. Let's see if we can get some consistent results here, Joe. About eight. Okay, we'll try it again because it seems to act silly after moving about five and a half. There must be some something on the surface that if it sits there a while it kind of gloms on to it and then once I get it moving it isn't there so much. So somewhere between five and a half and six, right? And then it starts to move. Phil, you agree with that? Something like that unless we let it sit for a while. So I won't let it sit for a while. Five, five and a half. So somewhere around five and a half or six it'll start to move again. I'm going to do something. I'm going to press down on this. Now what's its weight? Has the weight gone up? How'd the weight go up? What's my fingertip weigh? It depends on whether it's just been in my nose or not. It doesn't weigh much. I'm pressing down. I can press pretty hard. What's the weight of this? Does my finger change the weight of that? I still want to ask. Answer my question. Don't pull an owl on me. What happens to the weight of this, the little board and the two masses there when I press down? What happens to the weight of those things? Nothing. Is there a new force on here that I need to draw in? Well, yeah, of course. It's my finger. So I'm pressing down on it with one finger worth of force. Maybe we'll call that FF. I'm going to give this an F applied, force applied. That's the pole there we've got going sideways. There's my finger pushing down. The weight doesn't change because that's a factor of the mass of the thing sitting there. That doesn't change. So why would its weight change? Does anything else need to change now? The normal force, it had better get bigger. It needs to be that big plus that big. That normal force has to equal the weight we had there, the force I'm exerting with my finger. Yeah, my finger has a little bit of mass, but not much. So now let's see what happens, Joe. Let's retest it since we see it gets funny when it sticks for a little bit. All right, so that's six and a half. Now I'll press down. Let's get here in a minute. I wish Malcolm was here. Well, what time will it be? Malcolm could do this, couldn't he? Malcolm lifts weights. He tells us that. It's probably got a half. Huh? It's probably got a half because of it. There's funny. That's like a world record if I ever saw one. So I don't think since the weight didn't change and the maximum force I had to apply is clearly, in fact, it's off the scale now. I still couldn't even get it to move. It doesn't appear the maximum friction has to do with the weight. It appears more likely. It has to do with the normal force because that increased and that did increase the maximum static friction I had to apply. And we can do a lot of other tests that are much more quantitative than that. I don't know how much force I pushed down with. Once the normal force went up. But if we could test this much more carefully we would indeed find that this maximum peak point here this maximum static friction would indeed be a factor of the normal force. In fact, they're directly proportional. So I could write instead of that little squiggle which means has something to do with I could actually write is proportional to. Have you seen that symbol before in math? Some of you have and some of you haven't, I bet. It means is proportional to. Means that this peak is a linear function of the normal force. If I double the normal force either by doubling the weight or putting the weight on and pushing down with the same amount of force equal to the weight either way if I double the normal force I'll double that peak maximum friction. It's tough to show with this little thing on a crummy tabletop but if we could do that test carefully that's indeed what we'd see. Anytime I have a symbol that means is proportional to I can take that out replace it with an equal sign and a constant. Then I can make a direct calculation between the two. It turns out we call that the coefficient. No, that's a mu. It's a Greek letter mu. It's much like a U with a real long front tail. Our M came from that but that's a Greek letter mu. Remember we never write out these Greek letters. Reminds us that's the limit of the static region. So if I do anything to increase the normal force which means I could increase the weight that would increase the normal force or I could apply more force here downward myself that would increase the normal force. Anything, any combination of those is going to increase where this peak happens. The bigger the normal force the higher up this line goes. This one for one line just keeps going higher and higher and higher the higher the normal force gets. And in fact for static friction we could say static friction itself now notice I don't have any max written on there static friction is always less than or equal to mu s times M equal to, because we're at the maximum point thing than that we're down somewhere on this one for one slope this maximum static friction equal to this coefficient of static friction you got to figure we're going to have to know something more about that but for right now it just turns out that we do this measurement we set the normal force to something measure how much static friction we do that for a whole bunch of different normal forces measure the maximum friction force and then we can calculate that static coefficient. We could do that in the lab if we didn't have so many other busy things to do. The other region of interest I guess is this kinetic region where once it's moving it turns out no matter how hard you pull the friction force pulling back is pretty much the same it doesn't really change it wobbles a little bit but if I pull 8, 9, 10, 20 if I get Malcolm in here go to 25 if I get Malcolm and Samantha we go to 29 it doesn't matter the static or the kinetic friction will be pretty much the same no matter how much more I apply so we can also say there must be some kinetic friction that we could calculate it is also proportional to the normal force but it turns out the proportionality constant is different well you can see that because this friction force tends to drop down in fact in every situation I can think of mu k is less than mu s if nothing's accelerating yet if nothing's broken loose if we don't have this one surface sliding over the other there's going to be more friction than when we do get things moving and that's what you experience when you shove something across the floor try to get it refrigerator moving or something big effort to get it moving but then you try real hard not to let it stop again because now it's a little bit easier until you get it to where you're going you know that from pushing stuff across the floor so let's see maybe a little bit more word about these coefficients they're both very much the same in that they're essentially constant but there's some things we really need to understand with these coefficients let's be a little more thorough we'll say coefficients of friction whether static or kinetic there's a couple things that are true besides just the generality that the kinetic is generally less than the static coefficient of friction what you have to realize is when we talk about the difference between this static region and this kinetic region we're only looking at one thing we're not looking at the object necessarily itself and whether it's moving or not because I could do the same experiment by somehow holding this thing still and pulling the table underneath it and I would still get the same kind of friction measurements there if I could do that without much difficulty so it's not a factor of whether this thing is moving or not it's a matter of whether these two surfaces in contact are moving over each other it's this little wooden block moving over the tabletop that's important that's the difference between the static region when those two surfaces aren't moving over each other and the kinetic region when those two surfaces are moving over each other we don't look at the object and whether it's moving or not necessarily what we look at is the two surfaces in contact in fact this depends very very much on surfaces in contact remember I told you friction was a contact force we only have friction if we have two surfaces in contact if those surfaces are not moving and I mean not moving relative to each other not moving relative to each other I don't care which one's actually moving which object I don't care if one object's moving and the other isn't I don't care if they're both moving a little bit all I care is about what's happening if the surface is in contact that's where the friction is and that's where our concern is not moving relative to each other that's a static friction situation if they are moving relative to each not over other that's a kinetic friction situation that's the dividing line between these two regimes here you look at the two surfaces in contact where the friction is remember that the normal force is also a contact force with two surfaces in contact and in this case we're talking about the very two same surfaces it's the normal force at the surface where the friction is occurring that we're talking about here one other thing is very true about these coefficients of friction very much on what the surfaces are I'm trying to pull something across the floor and then I come in and well we even saw it change somehow here there's something weird that's on the surface but I'm really serious about this I have to clean these surfaces I have to clean them off of alcohol let them dry, be very careful where I touch them because all kinds of weird stuff can happen but if I grease the table if I let you guys borrow the table how many of you guys are living alone not living at home anymore Joey so if I let you bother this table because bachelors don't know how to clean anything I let you borrow this table for say a week or two and come back pretty greasy after that wouldn't it there'd be spaghetti chocolate milk yeah there we go and so we have entirely different test values for the maximum static friction and the kinetic friction it took to get that to move over so if I took the surface and I laid over it a real sticky foam rubber or something and then re-ran the test that'd be completely different again it very much depends upon what surfaces are in contact it's very different wood on fermica or in Joey's case wood on greasy fermica or say rubber on that pretty important one don't you think because that tells you how well your car tires stick when you're going around corners we know that if we don't have enough friction force on a corner you can't go around a corner where you're looking at centrifugal force the other day very much depends upon what the co-efficient friction or what the surfaces are that are in contact what would be nice then is if every time we need to do some kind of friction problem where we have some problem we understand friction to be a part of it it'd be very nice if we didn't have to re-test it every single time we have two surfaces in contact it'd be nice if somebody would test some surfaces say rubber on steel or tennis shoe rubber on ice or concrete on asphalt be nice if somebody would do that test for us and then just let us know what the coefficients are so we can do the calculation wouldn't that be nice well it turns out that a lot of those calculations have been done a lot of those tests have been run and this is the only way you can get these coefficients to do the test in your book on page 175 if you have your book if you don't, I can put it up on the screen why don't I go ahead and do that anyway trick you to one close enough nothing yet everybody wants to come up and gather around my monitor let's say you said I'm not going to camera is the light there in the right spot? the light is in your mouth no, the screen is there that's just how much light that is looking at you isn't it the lens is here so that's not the case I think we don't actually have this let's see where's my choice here it was blinking green before but now it's blinking green again there we go it was just sleep see if you don't bring the books I don't know how to do this kinetic and static coefficients so we see mu k that's connect what does that kinetic mean again, that k? what's that mean? what's moving? the two surfaces relative to each other I don't care what object is moving I care whether the surface is in contact or moving static coefficient means they're not moving the two surfaces are stuck to each other steel on steel well that's the kind of thing you'd want to know if you were building some machinery like this is what's going on with your pistons in the piston cylinders in your car these are actually kind of high numbers so you might want to put some oil in your car to decrease that a little bit that would be then lubricated steel on steel which would be a very different number copper on glass poison very important ones here rubber on concrete there we go at the bottom that's your car tires on the road surface we get pretty high coefficients of friction about the same but the static one is definitely definitely greater as most of you well that's why you don't want your tires spinning because the static coefficient is higher than the kinetic coefficient the tires are spinning your tires are spinning on the road surface that's a kinetic friction situation and typically the kinetic friction is less it's saying there are both about one but well maybe with concrete it is about that with asphalt it's very definitely true that the kinetic coefficient is less than the static coefficient and if you need other numbers than that there's a whole bunch of other publications that will tabulate a whole bunch of those things so you don't have to always look them all up alright so we need to do some problems with that so let's try a couple problems here another one with my car we like to drive in our car places so here's my car about a thousand kilograms am I in it or am I not in it a thousand kilograms I'm going about 30 meters per second I slam on the brakes lock up the wheels so I'm skipping them lock up the wheels because I panic when I need to stop I'm like you guys you know if I'm not squealing the tires when I stop I'm squealing the tires when I start I'm not going to meet the girl in my dreams so you've got to squeal those tires fellas so I lock up the wheels and I'm skidding coefficient of friction between my car tires and whatever surface I happen to be on let's say it's 0.8 kind of low much lower than rubber on concrete was so maybe I'm on a dirt road roads we have right now there's a lot of grit on them that's going to lower the coefficient of friction it's a lot easier to skid out when there's grit all over a road and of course I do that to bring myself to a stop how far do I travel in that skid until I come to a stop there's my question before we've done problems where somebody's moving and then they're not moving and we could figure out the acceleration or the distance or any of those type of things we needed so we're talking about what force is it that causes me to stop I've locked up the tires my tires are skidding over the road surface so there's a big friction force backwards that's what's slowing me down is that kinetic friction or static friction Joe says kinetic yeah my tires are skidding over the road the car is moving but that's not what matters what matters is what are the two surfaces doing with each other so my tires are skidding over the road surface that's a kinetic friction situation I'll skid before I come to a stop remember taking driver dead and they said stopping distance at certain speeds is so far as if you can calculate that you see a little boy run across the street chasing the ball I always do those calculations real fast but by the time I'm done I'm hidden there goes one more tuition fallar which is lost there how are we going to do this problem how are we going to get to this distance traveled we have initial velocity final velocity we're looking for distance that kind of sounds like the constant acceleration problems we were doing I told you this friction force when the two surfaces are sliding is fairly constant so if the forces are fairly constant the acceleration is fairly constant so we could do this as a constant acceleration problem so we have initial velocity final velocity we're looking for distance it's a constant acceleration problem how do we solve constant acceleration problems remember we've got those four equations but to work the four equations what do you need I already said constant acceleration you need three things there's five possible variables we've got three of them involved two we have one we're looking for so we need find the one thing we're looking for one thing that we know before we can do this is a constant acceleration problem remember there's only five possible variables in a constant acceleration problem we've got three of them so there's only two other possibilities what are they time how long is this acceleration going on or the acceleration itself we need one or the other of those then we know what equation you use we just look it up on our table and find the distance we traveled which one of those can we get and how time it takes to come to a stop or the acceleration we undergo to do this stop what good will that do because that's not either one of these when I say you're wrong I'm just asking you what good will that do I can find the force of friction I've got the canade but what good will it do time or the acceleration then we can do this then I can find the distance I got to find either one of these which one can I find now Mike was throwing out some stuff but I don't know that it was going anywhere I'm saying he's wrong I'm just not sure it was going anywhere and let's see some of the forces now let's do the usual let's call that x call that y so the sum of the forces in which direction why the x direction because we're looking for acceleration in the x direction this delta s is actually in the x direction here so it sounds like we at least ought to start there in fact maybe that's what we're looking for that would be our acceleration in the x direction which changes s to an x if you want no big deal it's just an arbitrary choice of a letter we've got the mass if we can find the acceleration we can do this problem so it all depends over here if we can sum the forces in the x direction what do we need before we sum the forces Phil now give me your usual answer we need to best sum the forces a free body diagram we don't have the right forces we don't have all the forces in the problem how are we going to sum the forces we can't just guess at them we got to think and make sure we got them all any forces any forces on the car who spoke up or who grabbed them Phil's starting to figure out how to avoid getting called on later jump in just say wait any time I ask a question just say wait and then go back to sleep any forces on that car got to be a normal force otherwise it would accelerate towards the center of the earth normal force between what two surfaces normal force is a contact force the tires in the ground there's only surfaces in contact in fact that's our surfaces of interest any other forces which direction opposite direction of the movement is the stationary ground the car tire remember the car tire is not turning it's moving but it's not turning so this surface is sliding over that surface friction opposes that so the friction will be back that way okay on it because this is a situation where two surfaces are sliding over each other yeah the car is moving and yeah the wheels moving with the car but the two surfaces are what we look at one surface is sliding over the other surface that's a situation of kinetic friction no other ways about it what other forces don't bother some of the forces until you're done with the free body diagram you don't know now remember it's got to be anytime we put a force up there you've got to tell me what's causing it Phil, oh you're awake again you're going to just say normal no you're going to say weight go back to sleep I can go put my hand on the previous movement well you could stick your head out you hit by a car tire for a second slide on the brakes so I can go back here before I put the brakes on I can roll down the back window stick my hand out the back touch the previous movement Phil you want to you want to just say weight and leave it at that don't forget no forces go on here unless you can tell me what I can touch that causes that force I can't touch previous movement I can't touch acceleration I can't touch circular motion like we were trying to do yesterday we wrestled with that a little bit forces are only caused by ropes surfaces people reaching in and pulling or pushing that's it sooner or later you're done you can't keep putting forces on forever sooner or later you're done we're done there are no other forces in this problem so some of the forces are in the x direction that's the x direction that's the force in the opposite direction so it's minus fk minus because I chose to the right positive and this force pushes to the left there aren't any other forces in the x direction times acceleration in the x direction well that's what we're looking for so we've got the mass friction force how big is it? if we can't figure that out we can't figure out this acceleration how big is that friction force? you have mu kinetic sure do friction mu kinetic right there so that might help a little bit minus still stays there minus mu k the coefficient of kinetic friction times and the normal force so I don't know maybe we're a little bit closer well we don't have the normal force where do you get the normal force? you get the normal force from your free body diagram there's no other place to get it in fact we need to sum the forces in the y direction well there is no y acceleration it's going on level ground it continues to do so so I know in this case n equals w if the ground isn't level n doesn't equal w so don't just assume that in this case n equals w for how we find w do I give it to you? we got the mass we don't have the weight mg equals m a it doesn't matter it does matter then in determining stopping distance if the mass doesn't matter what matters most is what kind of tires do you have on what kind of surface that's what matters the most oh also matters which planet you're on for some of you we're not sure where that is now we can figure out the acceleration now you can figure out the stopping distance so go ahead and finish the problem take a couple seconds to finish the problem we're going to have a calculator you called for help you called up your mom said mom calculate this quick figure out the acceleration then we've got a good situation here we don't need the time nor do we find it directly we can find the time once we found the acceleration but that's just an we need to find out what what was it that's more heading towards that little kid finish the calculation remember we're looking for delta s yeah you're saying oh oh his eye real big his throat is solid he can't move check the acceleration the acceleration is not right and your delta s isn't right maybe make those delta x since we did pick that at the x direction but we might as well be consistent especially since we're taking notes and chalk classes after this you have to drive home it's a long way so that's going to be what two stops, three stops maybe stop to pick up more of the pizza and you agree Mark, who would you check with nobody you know what to do here that I gave you that's on your calculator g is what it always is so you can find that then when you find that there's three things you know one thing you don't use your constant acceleration did it work who would you check with now you agree Tyler, you guys agree now Patrick almost what did you get for a just to make sure nope nope what there we go, got it all finally 8.5 what's the minus mean we picked the positive effect on his x the acceleration is negative to the left what we typically call deceleration now that you've got the acceleration is now just a constant acceleration problem that you can finish and we got for a stopping distance 57.4 meters which is lucky the kid was standing at 57.6 meters so scared to hell which is cool teach him a lesson don't run out the street alright we don't have much time I don't see you until Monday so I have to give you something that will consume at least several hours over the weekend see if I can keep you busy enough keep you out of jail so here's the problem there's a wall on the floor two kilogram box one kilogram box is tied to the wall with a titanium cable you are pulling on the bottom box with your full might I redlined the scale today 20 newtons I want you to find oh wait two more things coefficient of friction right there UK is 40 for any time two surfaces are in contact there can be friction UK is also box is doing otherwise we wouldn't have kinetic friction we'd have static friction because if it's moving it's moving over that surface and it's moving under that surface so find two things if you don't don't bother coming for the rest of the semester and that's the last week next week before spring break isn't it man yeah things are flying find the acceleration of the two kilogram box what's the acceleration of the one kilogram box zero it's tied to the wall and the tension in the cable back here titanium is expensive I don't want to buy a thicker cable than I need to got the problem that dude on your forehead when you come on Monday if I see it there you can come in however is there over forehead what are we going to do fifth thing yeah Allen's got a hat on you have bigger equations that's why you need to get into graduate school when your older equations get bigger because you have more forehead to put them on alright if you don't make your time with it when you're done I'll be in my office I guess